This week I have been studying the paper ‘A New Realisation of Quantum Geometry’. I’ll review the paper in the next post and follow up that with an analysis of the area operator in the SU(2) case.
What I’m posting at the moment is some exploratory work looking at the behaviour of the Wigner D matrix elements and U(1)area operator using python and sagemath.
Below I look at the general behaviour of the Wigner D matrix elements:
Below Here I look at the behaviour of the spectrum of the area operator with U(1).
Below I look at the how the area varies with μ for the values 0.1, 0.3, 0.5:
- Exact and asymptotic computations of elementary spin networks (quantumtetrahedron.wordpress.com)
- State Sums and Geometry by Frank Hellmann (quantumtetrahedron.wordpress.com)
- The length operator in Loop Quantum Gravity by Bianchi (quantumtetrahedron.wordpress.com)
- Semiclassical analysis of Loop Quantum Gravity by Claudio Perini (quantumtetrahedron.wordpress.com)